SOLUTION: The volume of cube is increasing at 20.0 cm^3/min. At the instant when its volume is 729 cm^3, what is the rate of change of its edge? Round the answer to 3 decimal places.

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Question 860001: The volume of cube is increasing at 20.0 cm^3/min. At the instant when its volume is 729 cm^3, what is the rate of change of its edge? Round the answer to 3 decimal places.
Answer by Alan3354(69443) About Me  (Show Source):
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The volume of cube is increasing at 20.0 cm^3/min. At the instant when its volume is 729 cm^3, what is the rate of change of its edge? Round the answer to 3 decimal places.
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V = s^3
s+=+V%5E%281%2F3%29%29
ds/dt = (1/3)*V^(-2/3)*dV/dt
ds/dt = (1/3)*729^(-2/3)*20
ds/dt = (20/3)/81 = 20/243
ds/dt =~ 0.0823 cm/min